Security Measures for Assessing Vulnerability to Large Deviations and Voltage Collapse in Electric Power Systems

在许多大型工程系统中，面对随机干扰，使系统状态保持在可接受的工作点是非常重要的。对于电力系统分析，评估小随机负荷变化的影响依赖于检查线性化系统在运行兴趣点附近的行为。然而，随机微分方程中大偏差现象的结果表明，在某些条件下，这种线性化分析可能是不够的。虽然线性化的系统（没有随机干扰）可能是渐近稳定的，但干扰的存在导致状态表现为扩散过程，在平衡附近“徘徊”。如果非线性系统中稳定平衡点的吸引区域有一部分边界足够接近平衡点，则该状态最终可能离开吸引集。确定性的动力学随后占据主导地位，将状态推离期望的操作点，导致“大偏差”。本研究将把随机摄动系统大偏差的最新理论成果应用于电力系统安全评估问题。一个主要的目标将是发展一种措施，表明易受电压崩溃的影响，这是一种观察到的大偏差效应，标准的小干扰稳定性分析是不够的。

In many large engineering systems it is important to maintain the system state at an acceptable operating point in the face of random disturbances. For power system analyses, evaluation of the effect of small random load variations has relied on examining the behavior of the linearized system about the operating point of interest. However, results on large deviation phenomena in stochastic differential equations indicate that under certain conditions, such linearized analysis may not be adequate. While the linearized system (without the random disturbance) may be asymptotically stable, the presence of the disturbance causes the state to behave as a diffusion process, "wandering" about the equilibrium. If the region of attraction for the stable equilibrium in the nonlinear system has a portion of its boundary sufficiently close to the equilibrium, the state may eventually leave the attracting set. The deterministic dynamics then dominate, pushing the state away from the desired operating point, resulting in a "large deviation." This research will apply recent theoretical results on large deviations in randomly perturbed dynamical systems to the power system security assessment problem. A primary goal will be to develop a measure which indicates vulnerability to voltage collapse, an observed large deviation effect for which standard small disturbance stability analyses are inadequate.